Solution Of Heat Flow Equation Research Articles

Subsurface Temperature Prediction from Multilayer Solution of Heat Flow Equation: A Case Study of Anambra Sedimentary Basin, Nigeria

Subsurface Temperature Prediction from Multilayer Solution of Heat Flow Equation: A Case Study of Anambra Sedimentary Basin, Nigeria

Algorithm Based on Convex Programming Method for Optimum Heat Input Control in Arc Welding

A simple mathematical method for the estimation of the optimum heat inputs in arc welding has been developed in the present work, the optimization problem is to make the temperature field coincide with the requirement during welding. In the expression of the problem, an analytical solution of heat flow equation is applied for the calculation of the temperature field in welding, and the objective function is defined as the difference between calculated and required temperatures. The problem is expressed as the quadratic function of heat inputs and it results in the convex programming problem, and it is clarified that the global optimum is certainly obtained by using Kuhn-Tucker conditions in the non-linear programming method. Furthermore, the propriety of the optimizing algorithm is evaluated experimentally by a bead-on-plate welding test, and it is concluded that the algorithm proposed in the present work is reliable and useful enough to determine the optimum heat input pattern in arc welding process.

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An algorithm for optimal heat input control in arc welding has been discussed in this paper.An optimization problem of the temperature field during welding has been proposed and tackled in order to estimate an optimal sequence of heat inputs. In the expression of the problem, the analytical solution of heat flow equation is used for the estimation of temperature field, and the objective function is defined as the difference between calculated and required temperatures.The following two typical optimization problems have been investigated. The objective in the first problem is to make the temperatures at some given times and points coincide with the required temperatures, and the objective in the second problem is to make the maximum temperatures at given points coincide with the required ones.As the result of this work, it is made clear that the convex programming is a powerful means of solving the first problem and the steepest descent method is useful for the second problem.